nutlope/llamatutor ? reverse-engineered prompt

Build me an open source AI personal tutor web app that feels simple and polished.

I want a landing page and a main chat experience where someone can ask a question, get a clear answer, and have the tutor pull in helpful web search results when needed. Make it look modern and friendly, with a clean dark or light style, responsive layout, and smooth chat interactions on desktop and mobile.

Use the current best setup for a Next.js app with TypeScript and Tailwind, and wire it up so the tutor can talk to a Llama 3.1 model through Together AI. If you need current docs for the APIs or setup details, look them up online. Also include basic analytics and observability hooks if they fit naturally.

It should feel like a real product people can use right away, with a nice homepage, a working chat flow, and room to grow later with things like follow up questions and sharing.